Some Nonlinear Problems in Transonic Helicopter Acoustics.

Abstract : The nonlinear potential equation that determines the near aerodynamic and far acoustic fields of a hovering transonic helicopter blade is derived. Properties of this equation provide a qualitative description of characteristic surfaces associated with the nonlinear flow field. A simple linearized acoustic formula is developed; a nonlinearization scheme is then applied to this formula, and the linear and nonlinear acoustic pressure profiles, including propagating acoustic shock waves, are numerically determined and compared with experimental data. A tentative conclusion is that the radiated sound field should become measurably different when the blade tip first punctures the sonic surface associated with the rotor differential equation. This conjecture is suggested by the mathematical properties of the rotor equation and recent experimental work. (Author)